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The selectivity or sharpness of series resonant circuit is measured by quality factor or Q factor.It is defined as the ratio of the voltage across the coil or capcitor to the applied voltage.In other words it refers to the sharpness of tuning at resonance.

Q = voltage across L or C ( in volts) / applied voltage ( in volts )

Q = 1/ R * ( L/C)^ 0.5

Q is just a mere number having values between 10 to 100 for normal frequencies.So it has no unit. Circuit with high Q values would respond to a very narrow frequency range and vice versa.Thus a circuit with high Q value is sharply tuned while a circuit with low Q value has a flat resonance.Q factor can be increased by having a coil of large inductance but of small ohmic resistance.

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